England play France in the World Cup quarter-finals on Saturday (19:00 GMT), with 52-year-old Southgate having already led the Three Lions to the 2018 semi-finals and the Euro 2020 final.
"I think people underestimate how good a manager Gareth Southgate is," Phillips said.
"I have been with England for three years and he has been amazing."
Southgate began his reign as England manager in October 2016, winning 49 and losing 13 of his 80 games in charge since.
But the defeat by Croatia in the last four of the 2018 World Cup in Russia, followed by another by Italy on penalties in the Euro 2020 final, led to questions about Southgate's ability to get the most out of his talented squad.
"How he has nurtured this team to winning games and one of the best countries in the world at playing football. A lot of people don't give him credit for that," continued Phillips.
"He has got very tough decisions to make. He has unbelievable players that he has to leave on the bench.
"I understand it is a very hard position he is in, but he has been unbelievable since I've been with England. He is an unbelievable man-manager."